Some boundary value problems for an equation of the third order parabolic-hyperbolic type in a pentagonal area

This article is an example of the application of methods for constructing solutions of integral and differential equations. Here we consider the equation of parabolic-hyperbolic type $\left(\frac{\partial}{\partial x} + \frac{\partial}{\partial y} \right)(Lu) = 0$ in a pentagonal area. We prove a theorem on the unique solvability of a set of two tasks.